Differential Equations
Go on a grand tour of differential equations and get the hands-on experience needed to master the essentials.
Differential Equations in a Nutshell
Our First Equation
Modeling: The Drag Equation
Separate and Integrate
Application: Molecular Motor
The Phase Portrait
Concavity and Partial Fractions
Application: In the Chem Lab
Capstone: Vampires of Cancelvania
Direction Fields
Integrating Factor
Application: A Mixing Problem
The Potential
Application: Fluid Flow
Capstone: The Great Escape
The Phase Plane
The Matrix Exponential
Application: Underdamped Springs
Non-Diagonalizable Matrices
Review: Math of a Salesman
Nonhomogeneous Systems: Part I
Nonhomogeneous Systems: Part II
Challenge: Floquet Theory
Equations of Order Two
Application: RLC Filter
Challenge: Higher-Order Equations
Application: Hangin' Around
Application: Beam Me Up!
Application: Get Your Motor Runnin'
Challenge: Why's The Sky Blue?
Course description
Differential equations show up in just about every branch of science, including classical mechanics, electromagnetism, circuit design, chemistry, biology, economics, and medicine. From analyzing the simple harmonic motion of a spring to looking at the population growth of a species, differential equations come in a rich variety of different flavors and complexities. This course takes you on a grand tour of some of the most important differential equations of the natural sciences, giving you the hands-on experience needed to master the essentials.
Topics covered
- Applications in Engineering
- Applications in Physics
- Direction Fields
- Euler's Method
- Integrating Factors
- Linear Systems
- Matrix Exponential
- Modeling
- Perturbation Method
- Phase Portraits
- Separable First-Order Equations
- Wronskian Determinants
Prerequisites and next steps
You’ll need a grasp of the basic derivative and integration rules covered in a first semester calculus course. Integration techniques are useful to know, but not necessary. Knowing basic linear algebra up to eigenvalues and eigenvectors and multivariable calculus up to gradients is essential.